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Properties

Label 1342.2.a
Level $1342$
Weight $2$
Character orbit 1342.a
Rep. character $\chi_{1342}(1,\cdot)$
Character field $\Q$
Dimension $49$
Newform subspaces $14$
Sturm bound $372$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1342 = 2 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1342.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(372\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1342))\).

Total New Old
Modular forms 190 49 141
Cusp forms 183 49 134
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(11\)\(61\)FrickeDim
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(9\)
\(+\)\(-\)\(-\)$+$\(4\)
\(-\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(8\)
Plus space\(+\)\(20\)
Minus space\(-\)\(29\)

Trace form

\( 49 q - q^{2} + 49 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 41 q^{9} + O(q^{10}) \) \( 49 q - q^{2} + 49 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} + 41 q^{9} - 6 q^{10} + q^{11} - 14 q^{13} - 8 q^{14} + 8 q^{15} + 49 q^{16} + 14 q^{17} - 13 q^{18} - 12 q^{19} - 2 q^{20} - 8 q^{21} - q^{22} + 4 q^{23} - 4 q^{24} + 47 q^{25} - 2 q^{26} + 24 q^{27} - 8 q^{28} + 10 q^{29} - 4 q^{31} - q^{32} + 4 q^{33} - 10 q^{34} + 32 q^{35} + 41 q^{36} - 6 q^{37} - 6 q^{40} + 14 q^{41} + 24 q^{42} - 28 q^{43} + q^{44} - 2 q^{45} - 16 q^{46} - 12 q^{47} + 17 q^{49} - 31 q^{50} - 16 q^{51} - 14 q^{52} - 14 q^{53} + 8 q^{54} + 6 q^{55} - 8 q^{56} - 32 q^{57} - 22 q^{58} + 12 q^{59} + 8 q^{60} - q^{61} + 24 q^{62} + 49 q^{64} - 12 q^{65} - 4 q^{66} - 36 q^{67} + 14 q^{68} + 80 q^{69} - 16 q^{70} - 4 q^{71} - 13 q^{72} - 10 q^{73} - 14 q^{74} + 8 q^{75} - 12 q^{76} - 8 q^{77} + 8 q^{78} - 32 q^{79} - 2 q^{80} + 25 q^{81} - 10 q^{82} + 52 q^{83} - 8 q^{84} - 36 q^{85} - 20 q^{86} - 8 q^{87} - q^{88} + 42 q^{89} - 6 q^{90} - 56 q^{91} + 4 q^{92} + 24 q^{93} + 16 q^{94} + 24 q^{95} - 4 q^{96} - 46 q^{97} + 7 q^{98} + 13 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1342))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 61
1342.2.a.a 1342.a 1.a $1$ $10.716$ \(\Q\) None \(-1\) \(1\) \(-2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+4q^{7}+\cdots\)
1342.2.a.b 1342.a 1.a $1$ $10.716$ \(\Q\) None \(1\) \(-1\) \(-4\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-2q^{7}+\cdots\)
1342.2.a.c 1342.a 1.a $1$ $10.716$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1342.2.a.d 1342.a 1.a $1$ $10.716$ \(\Q\) None \(1\) \(3\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+2q^{7}+q^{8}+\cdots\)
1342.2.a.e 1342.a 1.a $2$ $10.716$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
1342.2.a.f 1342.a 1.a $2$ $10.716$ \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
1342.2.a.g 1342.a 1.a $3$ $10.716$ 3.3.148.1 None \(3\) \(-3\) \(-4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1342.2.a.h 1342.a 1.a $4$ $10.716$ 4.4.14656.1 None \(-4\) \(-2\) \(-2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1342.2.a.i 1342.a 1.a $4$ $10.716$ 4.4.48396.1 None \(-4\) \(-2\) \(0\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1342.2.a.j 1342.a 1.a $4$ $10.716$ 4.4.2225.1 None \(4\) \(-2\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1342.2.a.k 1342.a 1.a $5$ $10.716$ 5.5.3362852.1 None \(-5\) \(-2\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1342.2.a.l 1342.a 1.a $6$ $10.716$ 6.6.8248384.1 None \(6\) \(-3\) \(-4\) \(-9\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(\beta _{3}-\beta _{5})q^{5}+\cdots\)
1342.2.a.m 1342.a 1.a $6$ $10.716$ 6.6.136632976.1 None \(6\) \(2\) \(2\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
1342.2.a.n 1342.a 1.a $9$ $10.716$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(5\) \(6\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1342))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1342)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 2}\)